When do you add this 12" extension to handrails at the bottom of a stair run?
All the time? Or are there times you don't need it?
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Another question: Can this 12" extension run perpendicular to the stair run? That is, can it turn a corner for example?
Assume an IBC, commercial application.
This is going to depend on the Local Authority Having Jurisdiction (AHJ)
The model IBC, DOJ Adopted 2010 ADA & the last 3 "ANSI A117.1" all do NOT require the 12" extension at the bottom of "STAIR FLIGHTS", they are only required at the top of stair flights and top and bottom of ramps.
So to answer your question: You will need to check for local adoption as a modification from the model code.
As to when you can turn, handrail extensions are required to extend for the minimum required 12 inches in the same direction of the stair flight and ramp runs without any turn, until after the minimum extension requirement is met.
The exception to the requirement is when the handrail continues on to a stair flight or ramp run, as a continuous run.
So if your project has not modified IBC for this section, then once your handrail has met the sloped distance equal to the last tread, you would be good and at that point even if you add the non required level off run, you can turn it.
Now if your in a jurisdiction that requires the 12" level off at the bottom stair flights, then you would have to project a minimum of 12" prior to turning.